I have one question for you. What technique did you use to place the applique piece onto the background? Did you thread baste the piece on, pin it, glue baste it or did you use freezer paper templates and starch? The applique piece will not be completely flat anyway. What also might be happening is that you are some how slightly moving the applique piece or the background as you sew. You really don't need a real tight grip on your background material. The applique stitch also should not be so tight that it causes tiny puckers.